2. Fractions: Simplification, Multiplication & Division Lesson 1e Next

3. Fractions have two parts: A Numerator & A Denominator Fractions fractions Numerals such as,, and are called fractions. Numerator Denominator Since you cannot divide by zero, the denominator of a fraction can never equal zero. However, a numerator can equal zero. Next

4. Fractions Any fraction with the same nonzero numerator and denominator equals 1. Next

5. Fractions Any fraction with a denominator of 1 names the same number as its numerator. Next

6. Product Rule for Fractions Multiply the numerators. Multiply the denominators Next “” is a symbol for multiplication (X).

7. Examples : Multiplying Fractions Multiply the numerators. Multiply the denominators Next “” is a symbol for multiplication (X). Multiply: Click here to check your answers!

8. Examples : Multiplying Fractions Multiply the numerators. Multiply the denominators Next “” is a symbol for multiplication (X). Multiply:

9. Writing Fractions in Lowest Terms A fraction is in lowest terms when the numerator and denominator have no common prime factors. In each of the fractions below, what common prime factor do each the numerator and denominator share? The common factor is 3 The common factor is 2 The common factor is 5 The common factor is 3 Next

10. Writing Fractions in Lowest Terms: Example 1 The first step in writing fractions in lowest terms is to write the numerator and denominator as a product of prime factors. Write in lowest terms: Solution:  Write the prime factorization.  Write as a product of two fractions.  Any number multiplied by one is equal to itself. Next

11. Writing Fractions in Lowest Terms: Example 2 Write in lowest terms: Solution:  Write the prime factorization.  Divide the numerator and the denominator by common factors.  Write in lowest terms. 1 1 1 1 Next

12. Practice Next Click here to check your answers! Write the following in lowest terms:

13. Practice Next 1 1 1 1 1 11 1 Write the following in lowest terms:

14. More on Multiplying Fractions Sometimes after multiplying fractions your answer needs to be reduced to lowest terms. For example: Next 1 2

15. More on Multiplying Fractions To reduce fractions, you can often use a shortcut when multiplying. If possible reduce by dividing a denominator and a numerator by the same number(a common factor). Then multiply. For Example: Next 1 2 5 and 10 have a common factor of 5.

16. Examples : Multiplying Fractions Multiply and then write your answers in lowest terms. Next Click here to check your answers!

17. Examples : Multiplying Fractions Multiply and then write your answers in lowest terms. Next 1 21 2 1 2 1 2 2 5 1 2 2 9 1 4 1 4 1 1

18. Multiplying Mixed Numbers In order to multiply mixed numbers you must change all mixed numbers to fractions. For Example: Next 4 = 82 ???? Multiply the 2 & 4 Now add the 8 to the numerator 3. 8 + 3 = 11 11 5 = 204 ???? Multiply the 4 & 5 Now add the 20 to the numerator 1. 20 + 1 = 21 21

19. Multiplying Mixed Numbers Now that we can change mixed numbers into fractions, we can multiply mixed numbers. First, we change the mixed number to a fraction. Next, we multiply the fractions as we have learned previously. Next Example 1:Example 2: ? ?

20. Examples: Multiplying Mixed Numbers Multiply and then write your answers in lowest terms. Next Click here to check your answers!

21. Examples: Multiplying Mixed Numbers Multiply and then write your answers in lowest terms. Next 1 2 1 111 2 3 1 2 1 1 5

22. Dividing Fractions Now that you can multiply fractions, you can learn to divide fractions. Next Example 1: ? Lastly, we change the division to multiplication, and multiply the fractions as we have learned previously. First, we change any mixed numbers to fractions. The second step is to write the reciprocal of the fraction that follows the division symbol (That fraction is called the divisor).reciprocal Example 2: ? 1 2

23. Examples: Dividing Fractions Multiply and then write your answers in lowest terms. Next Click here to check your answers!

24. Examples: Dividing Fractions Multiply and then write your answers in lowest terms. Next 2 1 1 2

26. Definition: Reciprocal Two numbers whose product is 1 are reciprocals. The reciprocal of  is.  X = 1 The reciprocal of 7 is . 7 X  = 1 The reciprocal of 2  is 3 / 7 2  =    X 3 / 7 = 1 BACK